Goodwillie scored twice in the first half and notched his third of the game in injury time.
Ryan Dow was also on the scoresheet for the home side while Christie Elliot netted a consolation for the visitors.
Goodwillie had only scored once in his previous eight games before the game but McNamara was unsurprised by the striker's performance against Thistle.
"I never doubted he was capable of that," McNamara said. "I'm delighted for him. I hope scoring three goals can be a turning point for him.
"The fourth goal, especially, was a great finish after a great bit of play from Ryan Gauld and a ball across at pace from Stuart Armstrong.
"There's been a lot of pressure on him to come up here and perform.
"Hopefully the other boys - like Nadir (Cifti), Armstrong and (Ryan) Gauld - chipping in with goals has taken a bit of weight off his shoulder and the goals will come. I hope there's more to come."
Thistle boss Alan Archibald was unsurprised that Goodwillie has finally come good for United and suggested his side had done themselves no favours after some early mistakes.
"Goodwillie is clinical," he said. "He scored three goals and that's what that kind of money gets you."
"I don't know what he costs (in wages) but probably five or six of our players. And you see for yourself - he was the difference.
"But if your strikers aren't scoring you have to keep clean sheets and we made a couple of errors.
"Conrad (Balatoni) slipped for the first goal, which was disappointing because he had a good performance and we lost a goal from a set-piece.
"But apart from that we were the better team."